Published by Andree Larroquette, 2019-08-11 10:01:06

## **Description: ** Algebra 1 Unit 1

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4 has no solutions. Explain why. 11 © 2014 College Board. All rights reserved. a. For the triangle shown, Anna said that any value of x greater than 5 is possible. Explain Anna’s error. b. Write a compound inequality that represents all possible values of x. 23. Find a value for n so that the compound inequality −n < x < n has no solutions. 48 SpringBoard® Mathematics Algebra 1, Unit 1 • Equations and InequalitiesAbsolute Value Equations and Inequalities ACTIVITY 4 Student Distances Lesson 4-1 Absolute Value Equations ••Learning Targets: My Notes Understand what is meant by a solution of an absolute value equation. Solve absolute value equations. SUGGESTED LEARNING STRATEGIES: Paraphrasing, Create Representations, Think-Pair-Share, Note Taking, Identify a Subtask Ms. Patel is preparing the school marching band for the homecoming show. She has the first row of band members stand in positions along a number line on the floor of the band room. The students’ positions match the points on a number line as shown. Derrick Kia Mara Israel Laura Tania Antwan Nick Sam -10 -8 -6 -4 -2 0 2 4 6 8 10 1. Use the number line to write each student’s distance from 0 next to their name. For example, Tania is 2 units away from 0. Israel’s distance from 0 is also 2 units even though he is at −2. Derrick Laura Kia Israel Mara Antwan Tania Nick Sam © 2014 College Board. All rights reserved. The absolute value of a number is the distance from 0 to the number on a READING MATH number line. Using absolute value notation, Mara’s distance is |−3| and Antwan’s distance is |3|. Since Mara and Antwan are each 3 units from 0, Read |−3| as “the absolute value |−3| = 3 and |3| = 3. of negative three.” 2. Attend to precision. Write each person’s distance from 0 using absolute value notation. Absolute value equations can represent distances on a number line. MATH TERMS 3. The locations of the two students who are 5 units away from 0 are the solutions of the absolute value equation |x| = 5. Which two students An absolute value equation is an represent the solutions to the equation |x| = 5? equation involving the absolute value of a variable expression. Activity 4 • Absolute Value Equations and Inequalities 49ACTIVITY 4 Lesson 4-1 continued Absolute Value Equations My Notes 4. You can create a graph on a number line to represent the solutions of an absolute value equation. Graph the solutions of the equation |x| = 5 on the number line below. Then use the graph to help you explain why it makes sense that the equation |x| = 5 has two solutions. –5 –4 –3 –2 –1 0 1 2 3 4 5 Absolute value equations can also represent distances between two points on a number line. 5. In the student line, which two people are 4 units away from 1? Mark their location on the number line below. -5 -4 -3 -2 -1 0 1 2 3 4 5 The equation |x| = 4 represents the numbers located 4 units away from 0. So the equation |x| = 4 can also be written as |x − 0| = 4, which shows the distance (4) away from the point 0. In Item 5, you were looking for the numbers located 4 units away from 1. So you can write the absolute value equation |x − 1| = 4 to represent that situation. 6. What are two possible values for x − 1 given that |x − 1| = 4? Explain. 7. Use the two values you found in Item 6 to write two equations showing © 2014 College Board. All rights reserved. what x − 1 could equal. 8. Solve each of the two equations that you wrote in Item 7. The solutions in Item 8 represent the two points on the number line that are 4 units from 1. 9. How do the solutions relate to your answer for Item 5? 50 SpringBoard® Mathematics Algebra 1, Unit 1 • Equations and Inequalities

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